Top-K with a Heap

Keep only the largest k values by maintaining a small min-heap.

Algorithm

Steps

Store the heap in an array.
Compare parent and child indexes instead of building explicit tree nodes.
Swap only when the heap order is violated.
Print the deterministic final heap state for replay comparison.

Complexity

Time: O(n log k)
Space: O(k)

bounded heap For top-k largest values, a min-heap of size k keeps the current cutoff at the root.

Ruby DSA Implementation

basic.rb

def list_string(values) = "[#{values.join(', ')}]"
def heap_insert(heap, value)
  heap << value
  child = heap.length - 1
  while child > 0
    parent = (child - 1) / 2
    break if heap[parent] <= heap[child]
    heap[parent], heap[child] = heap[child], heap[parent]
    child = parent
  end
end
def heap_pop(heap)
  smallest = heap[0]
  heap[0] = heap.pop
  parent = 0
  loop do
    left = parent * 2 + 1
    right = left + 1
    break if left >= heap.length
    child = right < heap.length && heap[right] < heap[left] ? right : left
    break if heap[parent] <= heap[child]
    heap[parent], heap[child] = heap[child], heap[parent]
    parent = child
  end
  smallest
end
heap = []
[5, 1, 9, 3, 7, 2].each do |value|
  heap_insert(heap, value)
  heap_pop(heap) if heap.length > 3
end
puts list_string(heap.sort.reverse)

Implementation notes

The working heap is a Ruby Array used as a min-heap, starting from heap = [].
This page reuses heap_insert and heap_pop; both mutate the same heap array in place.
The input values are fixed as [5, 1, 9, 3, 7, 2], and the size bound is the literal 3.
Each value is inserted first with heap_insert(heap, value).
Immediately after insertion, heap_pop(heap) if heap.length > 3 removes the current minimum whenever the heap grows past the top-k size.
That means small values can enter briefly; the trace for value 2 ends back at [5, 7, 9] after trimming.
The replayed heap states are [5], [1, 5], [1, 5, 9], [3, 5, 9], [5, 7, 9], then [5, 7, 9].
The heap array itself is not descending sorted, so output uses heap.sort.reverse only for display.
list_string(heap.sort.reverse) prints the final top values as [9, 7, 5].

Output

[9, 7, 5]